Convolution and limit theorems for conditionally free random variables
We introduce the notion of a conditionally free product and conditionally free convolution. We describe this convolution both from a combinatorial point of view, by showing its connection with the lattice of non-crossing partitions, and from an analytic point of view, by presenting the basic formula...
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| Hauptverfasser: | , , |
|---|---|
| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
1 October 1996
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| In: |
Pacific journal of mathematics
Year: 1996, Jahrgang: 175, Heft: 2, Pages: 357-388 |
| ISSN: | 1945-5844 |
| DOI: | 10.2140/pjm.1996.175.357 |
| Online-Zugang: | Verlag, kostenfrei, Volltext: http://dx.doi.org/10.2140/pjm.1996.175.357 Verlag, kostenfrei, Volltext: https://msp.org/pjm/1996/175-2/p04.xhtml 
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| Verfasserangaben: | Marek Bożejko, Michael Leinert and Roland Speicher |
MARC
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| 520 | |a We introduce the notion of a conditionally free product and conditionally free convolution. We describe this convolution both from a combinatorial point of view, by showing its connection with the lattice of non-crossing partitions, and from an analytic point of view, by presenting the basic formula for its R-transform. We calculate explicitly the distributions of the conditionally free Gaussian and conditionally free Poisson distribution. | ||
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